MATA230 Geometry (5 cr)
Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024
Description
Hilbert's axioms and neutral geometry, Euclidean plane geometry, hyperbolic geometry, Poincaré model for hyperbolic geometry
Learning outcomes
After the course student
- knows the basic structure of axiomatic systems and the concept of independence for axioms
- understands the role of models for axiomatic systems
- can prove basic results in neutral geometry
- is aware of the common ground and the differences of Euclidean and hyperbolic geometries
- can use models to illustrate hyperbolic geometry
Description of prerequisites
Euklidinen tasogeometria on suositeltava, mutta ei välttämätön esitieto.
Study materials
Luentomoniste (Kurittu, Hokkanen, Kahanpää: Geometria)
Literature
- Hartshorne, R., Geometry : Euclid and beyond, Springer cop. 2000.; ISBN: 0-387-98650-2
- Greenberg, M.J., Euclidean and non-Euclidean geometries : development and history, W.H. Freeman cop. 1993. 3rd ed; ISBN: 0716724464
Completion methods
Method 1
Evaluation criteria:
Homeworks and Course exam.
Select all marked parts
Method 2
Evaluation criteria:
Final Exam
Select all marked parts
Parts of the completion methods
x
Teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Homeworks and Course exam.
Language:
Finnish
Study methods:
28h lectures, 7 exercise sessions
Study materials:
Lecture notes (in Finnish): Kurittu, Hokkanen, Kahanpää: Geometria
Literature:
- Hartshorne, R., Geometry : Euclid and beyond, Springer cop. 2000.; ISBN: 0-387-98650-2
- Greenberg, M.J., Euclidean and non-Euclidean geometries : development and history, W.H. Freeman cop. 1993. 3rd ed; ISBN: 0716724464
Teaching
9/5–10/29/2023 Lectures
11/8–11/8/2023 Exam
11/17–11/17/2023 Exam
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Final Exam
Language:
English, Finnish
Study methods:
Final Exam
Study materials:
Luentomoniste (Kurittu, Hokkanen, Kahanpää: Geometria)
Literature:
- Hartshorne, R., Geometry : Euclid and beyond, Springer cop. 2000.; ISBN: 0-387-98650-2
- Greenberg, M.J., Euclidean and non-Euclidean geometries : development and history, W.H. Freeman cop. 1993. 3rd ed; ISBN: 0716724464